-2x(3x-7)=-5x+10

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Solution for -2x(3x-7)=-5x+10 equation:


Simplifying
-2x(3x + -7) = -5x + 10

Reorder the terms:
-2x(-7 + 3x) = -5x + 10
(-7 * -2x + 3x * -2x) = -5x + 10
(14x + -6x2) = -5x + 10

Reorder the terms:
14x + -6x2 = 10 + -5x

Solving
14x + -6x2 = 10 + -5x

Solving for variable 'x'.

Reorder the terms:
-10 + 14x + 5x + -6x2 = 10 + -5x + -10 + 5x

Combine like terms: 14x + 5x = 19x
-10 + 19x + -6x2 = 10 + -5x + -10 + 5x

Reorder the terms:
-10 + 19x + -6x2 = 10 + -10 + -5x + 5x

Combine like terms: 10 + -10 = 0
-10 + 19x + -6x2 = 0 + -5x + 5x
-10 + 19x + -6x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-10 + 19x + -6x2 = 0

Factor a trinomial.
(-5 + 2x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {2.5, 0.6666666667}

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